The indentation of standard viscoelastic solids, that is, the three-element viscoelastic material, by an axisymmetric, flat-ended indenter has been investigated theoretically. Under the boundary conditions of flat-punch indentation of a viscoelastic half-space, the solutions of the equations of viscoelastic deformation are derived for the standard viscoelastic material. Their generality resides in their inclusion of compressible as well as incompressible solids. They cover the two transient situations: flat-punch creep test and load-relaxation test, in experimental tests of their applicability, nanoindentation and microindentation probes under creep and relaxation conditions yielded a modulus from 0.1 to 1.1 GPa and viscosity from 1 to 31 Gpa . s for a crosslinked glassy polyurethane coatings. For bulk polystyrene, the values vary from 1 to 2 GPa and from 20 to 40 Gpa . s, respectively. The analysis here provides a fundamental basis for probing elastic and viscous properties of coatings with nanoindentation or microindentation tests.